OSA's Digital Library

Optics Letters

Optics Letters


  • Editor: Alan E. Willner
  • Vol. 34, Iss. 9 — May. 1, 2009
  • pp: 1363–1365

Broadband CARS spectral phase retrieval using a time-domain Kramers–Kronig transform

Yuexin Liu, Young Jong Lee, and Marcus T. Cicerone  »View Author Affiliations

Optics Letters, Vol. 34, Issue 9, pp. 1363-1365 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (229 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We describe a closed-form approach for performing a Kramers–Kronig (KK) transform that can be used to rapidly and reliably retrieve the phase, and thus the resonant imaginary component, from a broadband coherent anti-Stokes Raman scattering (CARS) spectrum with a nonflat background. In this approach we transform the frequency-domain data to the time domain, perform an operation that ensures a causality criterion is met, then transform back to the frequency domain. The fact that this method handles causality in the time domain allows us to conveniently account for spectrally varying nonresonant background from CARS as a response function with a finite rise time. A phase error accompanies KK transform of data with finite frequency range. In examples shown here, that phase error leads to small ( < 1 % ) errors in the retrieved resonant spectra.

© 2009 U.S. Government

OCIS Codes
(300.2570) Spectroscopy : Four-wave mixing
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:

Original Manuscript: December 12, 2008
Revised Manuscript: March 25, 2009
Manuscript Accepted: March 30, 2009
Published: April 22, 2009

Yuexin Liu, Young Jong Lee, and Marcus T. Cicerone, "Broadband CARS spectral phase retrieval using a time-domain Kramers–Kronig transform," Opt. Lett. 34, 1363-1365 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. A. Rinia, M. Bonn, and M. Muller, J. Phys. Chem. B 110, 4472 (2006). [CrossRef] [PubMed]
  2. D. Y. Smith, J. Opt. Soc. Am. 67, 570 (1977). [CrossRef]
  3. K.-E. Peiponen, V. Lucarini, J. J. Saarinen, and E. Vartiainen, Appl. Spectrosc. 58(5), 499 (2004). [CrossRef] [PubMed]
  4. D. E. Aspnes, The Accurate Determination of Optical Properties by Ellipsometry, in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), pp. 89-112.
  5. V. Lucarini, J. J. Saarinen, K. E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).
  6. R. K. Ahrenkiel, J. Opt. Soc. Am. 61, 1651 (1971). [CrossRef]
  7. K. F. Palmer, M. Z. Williams, and B. A. Budde, Appl. Opt. 37, 2660 (1998). [CrossRef]
  8. C. W. Peterson and B. W. Knight, J. Opt. Soc. Am. 63, 1238 (1973). [CrossRef]
  9. D. W. Johnson, J. Phys. A 8, 490 (1975). [CrossRef]
  10. E. M. Vartiainen, K. E. Peiponen, and T. Tsuboi, J. Opt. Soc. Am. B 7, 722 (1990). [CrossRef]
  11. E. M. Vartiainen, H. A. Rinia, M. Muller, and M. Bonn, Opt. Express 14, 3622 (2006). [CrossRef] [PubMed]
  12. Y. X. Liu, Y. J. Lee, and M. T. Cicerone, J. Raman Spectrosc. (to be published).
  13. S. H. Lim, A. G. Caster, and S. R. Leone, Opt. Lett. 32, 1332 (2007). [CrossRef] [PubMed]
  14. L. Lepetit, G. Cheriaux, and M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995). [CrossRef]
  15. B. C. Chen and S. H. Lim, J. Phys. Chem. B 112, 3653 (2008). [CrossRef] [PubMed]
  16. G. B. Arfken, Mathematical Methods for Physics, 5th ed. (Academic, 2001).
  17. K. Ohta and H. Ishida, Appl. Spectrosc. 42, 952 (1988). [CrossRef]
  18. E. M. Vartiainen, J. Opt. Soc. Am. B 9, 1209 (1992). [CrossRef]
  19. T. W. Kee, H. X. Zhao, and M. T. Cicerone, Opt. Express 14, 3631 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited